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Root Mean Square00:57

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If in an experiment, data values have a probability of being both positive and negative, neither the arithmetic mean, the geometric mean, nor the harmonic mean can be used to calculate the central tendency of the data set. In particular, if the positive and negative values are equally likely, the arithmetic mean is close to zero.
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A cruise control system in a car is designed to maintain a specified speed automatically by adjusting the gas pedal. The system continuously measures the vehicle's speed and makes fine adjustments to the pedal to achieve this goal. The root locus method is particularly useful for understanding how the cruise control system's behavior changes under varying conditions, such as when the car goes uphill, downhill, or faces strong wind resistance.
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The construction of a root locus involves several key steps to analyze and visualize the behavior of a system's poles with varying gain. The number of branches in the root locus equals the number of closed-loop poles and is symmetrical about the real axis.
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Related Experiment Video

Updated: Aug 19, 2025

A Simple Protocol for Mapping the Plant Root System Architecture Traits
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A Simple Protocol for Mapping the Plant Root System Architecture Traits

Published on: February 10, 2023

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Novel seed generation and quadrature-based square rooting algorithms.

Amal Altamimi1,2, Belgacem Ben Youssef3

  • 1Department of Computer Engineering, College of Computer & Information Sciences, King Saud University, P.O. Box 51178, Riyadh, 11543, Saudi Arabia.

Scientific Reports
|November 29, 2022
PubMed
Summary
This summary is machine-generated.

We developed two new algorithms for faster square root calculations. One algorithm significantly reduces iterations by up to 84.42%, while the other achieves high accuracy in a single iteration, outperforming existing methods.

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Area of Science:

  • Computational Science and Engineering
  • Numerical Analysis

Background:

  • Square root approximation is crucial in many scientific and engineering fields.
  • Convergence speed of square root algorithms heavily depends on the initial seed value accuracy.

Purpose of the Study:

  • To propose two novel algorithms for efficient and accurate square root computation.
  • To improve the performance of existing square root approximation techniques.

Main Methods:

  • A novel seed generation technique using bit manipulation for initial square root approximation.
  • A quadrature-based square rooting method employing a rectangle for squaring and a lookup table for cosine values.

Main Results:

  • The seed generation approach reduced iterations by up to 84.42% for selected convergence methods.
  • The proposed square rooting algorithm achieves high accuracy in a single iteration.
  • The new algorithm offers lower computational latency compared to Newton-Raphson and Bakhshali methods.

Conclusions:

  • The proposed algorithms offer significant improvements in speed and accuracy for square root calculations.
  • Bit manipulation for seed generation and quadrature-based methods provide efficient alternatives for computational tasks.